x^2+23x=1023

Solution for x^2+23x=1023 equation:

x^2+23x=1023

We move all terms to the left:

x^2+23x-(1023)=0

a = 1; b = 23; c = -1023;
Δ = b2-4ac
Δ = 232-4·1·(-1023)
Δ = 4621
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{4621}}{2*1}=\frac{-23-\sqrt{4621}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{4621}}{2*1}=\frac{-23+\sqrt{4621}}{2}
$